Question 991538: Find an equation for the line with the given properties. Express the answer using the general form of the equation of a line.
Perpendicular to the line -4x + 5y = -23; containing the point (-3, 7)
a. -3x - 5y = -23
b. -4x - 5 = -4
c. -5x + 4y = -13
d. -5x - 4y = -13
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
Sort the equation out to y = mx + c form
-4x + 5y = -23
5y = 4x - 23
y = 4/5x - 23/5
Gradient = 4/5
Lines that are perpendicular have
gradients that multiply together
to give -1
m1 x m2 = -1
So,
4/5 x m2 = -1
m2 = -5/4
Using equation for a straight line
=> y - b = m(x - a)
with m = -5/4 and (a,b) = (-3,7)
y -7 = -5/4(x -(-3))
y - 7 = -5/4(x + 3)
y - 7 = -5/4x - 15/4
y = -5/4x - 15/3 + 28/4 (7)
y = -5/4x + 13/4
Multiply throughout by -4
-4y = 5x - 13
-5x - 4y = -13 (d)
Hope this helps :-)
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